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    <title>Slides | Peter Charlton</title>
    <link>https://peterhcharlton.github.io/slides/</link>
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    <description>Slides</description>
    <generator>Wowchemy (https://wowchemy.com)</generator><language>en-us</language><copyright>© 2025 Peter Charlton</copyright><lastBuildDate>Sun, 01 Jan 2017 00:00:00 +0000</lastBuildDate>
    <item>
      <title>Introduction to modelling arterial pulse waves</title>
      <link>https://peterhcharlton.github.io/slides/intro_to_pulse_wave_modelling_slides/</link>
      <pubDate>Sun, 01 Jan 2017 00:00:00 +0000</pubDate>
      <guid>https://peterhcharlton.github.io/slides/intro_to_pulse_wave_modelling_slides/</guid>
      <description>&lt;h2 id=&#34;an-introduction-to-modelling-arterial-pulse-waves&#34;&gt;An introduction to modelling arterial pulse waves&lt;/h2&gt;
&lt;p&gt;Peter Charlton, University of Cambridge, UK&lt;/p&gt;
&lt;p&gt;&lt;a href=&#34;https://peterhcharlton.github.io/talk/introduction-to-modelling-arterial-pulse-waves/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;peterhcharlton.github.io&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&lt;em&gt;&lt;strong&gt;To do:&lt;/strong&gt; Please go to this website, find this talk under &amp;lsquo;Talks&amp;rsquo;, and see the accompanying resources.&lt;/em&gt;&lt;/p&gt;
&lt;hr&gt;
&lt;h2 id=&#34;i-find-simulated-pulse-waves-useful-for&#34;&gt;I find simulated pulse waves useful for:&lt;/h2&gt;
&lt;ol&gt;
&lt;li&gt;Understanding physiological mechanisms&lt;/li&gt;
&lt;li&gt;Designing algorithms&lt;/li&gt;
&lt;li&gt;Investigating algorithm performance&lt;/li&gt;
&lt;/ol&gt;
&lt;hr&gt;
&lt;h2 id=&#34;accompanying-resources&#34;&gt;Accompanying resources&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href=&#34;https://peterhcharlton.github.io/slides/intro_to_pulse_wave_modelling_slides/&#34;&gt;The slides&lt;/a&gt;: click to expand images&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://app.sli.do/event/1zunclmb&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;The event poll&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://peterhcharlton.github.io/publication/simulating_pulse_waves/&#34;&gt;Accompanying paper&lt;/a&gt; (from which much content in this presentation is reproduced under &lt;a href=&#34;https://creativecommons.org/licenses/by/4.0/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;CC BY 4.0&lt;/a&gt;)&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;h1 id=&#34;part-1&#34;&gt;Part 1&lt;/h1&gt;
&lt;h2 id=&#34;an-introduction-to-pulse-wave-modelling-using-a-1d-model&#34;&gt;An Introduction to Pulse Wave Modelling using a 1D Model&lt;/h2&gt;
&lt;hr&gt;
&lt;h2 id=&#34;the-model&#34;&gt;The Model&lt;/h2&gt;
&lt;p&gt;&lt;a href=&#34;https://journals.physiology.org/cms/10.1152/ajpheart.00218.2019/asset/images/large/zh40101929420001.jpeg&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;img src=&#34;https://journals.physiology.org/cms/10.1152/ajpheart.00218.2019/asset/images/large/zh40101929420001.jpeg&#34; alt=&#34;A 1D Model&#34;&gt;&lt;/a&gt;&lt;/p&gt;
&lt;hr&gt;
&lt;h2 id=&#34;simulated-pulse-waves&#34;&gt;Simulated Pulse Waves&lt;/h2&gt;
&lt;p&gt;&lt;a href=&#34;https://journals.physiology.org/cms/10.1152/ajpheart.00218.2019/asset/images/large/zh40101929420005.jpeg&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;img src=&#34;https://journals.physiology.org/cms/10.1152/ajpheart.00218.2019/asset/images/large/zh40101929420005.jpeg&#34; alt=&#34;Example simulated pulse waves&#34;&gt;&lt;/a&gt;&lt;/p&gt;
&lt;hr&gt;
&lt;h2 id=&#34;model-limitations&#34;&gt;Model Limitations&lt;/h2&gt;
&lt;p&gt;&lt;strong&gt;Poll Question:&lt;/strong&gt; &lt;a href=&#34;https://app.sli.do/event/1zunclmb&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;What are the limitations of the model?&lt;/a&gt;&lt;/p&gt;
&lt;hr&gt;
&lt;h2 id=&#34;possible-limitations&#34;&gt;Possible Limitations&lt;/h2&gt;
&lt;p&gt;A few thoughts:&lt;/p&gt;
&lt;ol&gt;
&lt;li&gt;Periodic inflow, as opposed to normal heart rate variability&lt;/li&gt;
&lt;li&gt;Specified arterial properties, which may not be representative of a particular individual&lt;/li&gt;
&lt;li&gt;Not able to model venous flow&lt;/li&gt;
&lt;/ol&gt;
&lt;hr&gt;
&lt;h2 id=&#34;input-parameters&#34;&gt;Input Parameters&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;HR: heart rate&lt;/li&gt;
&lt;li&gt;SV: stroke volume&lt;/li&gt;
&lt;li&gt;LVET: left ventricular ejection time&lt;/li&gt;
&lt;li&gt;PFT: time of peak aortic flow&lt;/li&gt;
&lt;li&gt;RFV: reverse flow volume&lt;/li&gt;
&lt;li&gt;Diam: the diameters of the largest arteries&lt;/li&gt;
&lt;li&gt;PWV: pulse wave velocities&lt;/li&gt;
&lt;li&gt;MAP: mean blood pressure&lt;/li&gt;
&lt;li&gt;PVC: peripheral vascular compliance&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;h2 id=&#34;changing-inputs&#34;&gt;Changing Inputs&lt;/h2&gt;
&lt;p&gt;Which parameters would be most interesting to change, and why?&lt;/p&gt;
&lt;p&gt;Which are most relevant to vascular ageing?&lt;/p&gt;
&lt;hr&gt;
&lt;h2 id=&#34;changing-inputs-2&#34;&gt;Changing Inputs (2)&lt;/h2&gt;
&lt;p&gt;&lt;a href=&#34;https://journals.physiology.org/cms/10.1152/ajpheart.00218.2019/asset/images/large/zh40101929420003.jpeg&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;img src=&#34;https://journals.physiology.org/cms/10.1152/ajpheart.00218.2019/asset/images/large/zh40101929420003.jpeg&#34; alt=&#34;A 1D Model&#34;&gt;&lt;/a&gt;&lt;/p&gt;
&lt;hr&gt;
&lt;h2 id=&#34;changing-inputs-3&#34;&gt;Changing Inputs (3)&lt;/h2&gt;
&lt;p&gt;&lt;a href=&#34;https://journals.physiology.org/cms/10.1152/ajpheart.00218.2019/asset/images/large/zh40101929420002.jpeg&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;img src=&#34;https://journals.physiology.org/cms/10.1152/ajpheart.00218.2019/asset/images/large/zh40101929420002.jpeg&#34; alt=&#34;A 1D Model&#34;&gt;&lt;/a&gt;&lt;/p&gt;
&lt;hr&gt;
&lt;h2 id=&#34;virtual-subjects&#34;&gt;Virtual Subjects&lt;/h2&gt;
&lt;p&gt;We created:&lt;/p&gt;
&lt;ol&gt;
&lt;li&gt;Baseline virtual subject at each age&lt;/li&gt;
&lt;li&gt;Virtual subjects at each age with varying cardiovascular properties&lt;/li&gt;
&lt;li&gt;A publicly available &lt;a href=&#34;https://peterhcharlton.github.io/pwdb/pwdb.html&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;database&lt;/a&gt; of simulated pulse waves for 4,374 virtual subjects&lt;/li&gt;
&lt;/ol&gt;
&lt;hr&gt;
&lt;h2 id=&#34;comparison-with-_in-vivo_-data&#34;&gt;Comparison with &lt;em&gt;in vivo&lt;/em&gt; Data&lt;/h2&gt;
&lt;p&gt;&lt;strong&gt;Poll Question:&lt;/strong&gt; &lt;a href=&#34;https://app.sli.do/event/1zunclmb&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;How well did the model perform?&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&lt;a href=&#34;https://journals.physiology.org/cms/10.1152/ajpheart.00218.2019/asset/images/large/zh40101929420006.jpeg&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;img src=&#34;https://journals.physiology.org/cms/10.1152/ajpheart.00218.2019/asset/images/large/zh40101929420006.jpeg&#34; alt=&#34;A 1D Model&#34;&gt;&lt;/a&gt;&lt;/p&gt;
&lt;hr&gt;
&lt;h3 id=&#34;thoughts-on-performance&#34;&gt;Thoughts on Performance&lt;/h3&gt;
&lt;ul&gt;
&lt;li&gt;Increase in amplitude of second systolic peaks with age&lt;/li&gt;
&lt;li&gt;Disappearance of second peak of finger PPG with age&lt;/li&gt;
&lt;li&gt;Nonetheless, some marked differences between &lt;em&gt;in vivo&lt;/em&gt; and simulated waveforms.&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;For further details of the verification see the &lt;a href=&#34;https://peterhcharlton.github.io/publication/simulating_pulse_waves/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;accompanying article&lt;/a&gt;.&lt;/p&gt;
&lt;hr&gt;
&lt;h1 id=&#34;part-2&#34;&gt;Part 2&lt;/h1&gt;
&lt;h2 id=&#34;case-study-assessing-arterial-stiffness-from-the-photoplethysmogram&#34;&gt;Case Study: Assessing Arterial Stiffness from the Photoplethysmogram&lt;/h2&gt;
&lt;hr&gt;
&lt;h3 id=&#34;digital-wearable-device&#34;&gt;Digital Wearable Device&lt;/h3&gt;
&lt;p&gt;&lt;a href=&#34;https://upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Max_Health_Band.jpg/640px-Max_Health_Band.jpg&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;img src=&#34;https://upload.wikimedia.org/wikipedia/commons/thumb/d/dc/Max_Health_Band.jpg/640px-Max_Health_Band.jpg&#34; alt=&#34;&#34;&gt;&lt;/a&gt;&lt;/p&gt;
&lt;hr&gt;
&lt;h3 id=&#34;the-photoplethysmogram-ppg&#34;&gt;The Photoplethysmogram (PPG)&lt;/h3&gt;
&lt;p&gt;&lt;a href=&#34;https://upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Photoplethysmogram_signal_components.svg/640px-Photoplethysmogram_signal_components.svg.png&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;img src=&#34;https://upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Photoplethysmogram_signal_components.svg/640px-Photoplethysmogram_signal_components.svg.png&#34; alt=&#34;&#34;&gt;&lt;/a&gt;&lt;/p&gt;
&lt;hr&gt;
&lt;h3 id=&#34;changes-in-ppg-pulse-wave-shape&#34;&gt;Changes in PPG Pulse Wave Shape&lt;/h3&gt;
&lt;p&gt;&lt;a href=&#34;https://upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Classes_of_photoplethysmogram_%28PPG%29_pulse_wave_shape.svg/640px-Classes_of_photoplethysmogram_%28PPG%29_pulse_wave_shape.svg.png&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;img src=&#34;https://upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Classes_of_photoplethysmogram_%28PPG%29_pulse_wave_shape.svg/640px-Classes_of_photoplethysmogram_%28PPG%29_pulse_wave_shape.svg.png&#34; alt=&#34;&#34;&gt;&lt;/a&gt;&lt;/p&gt;
&lt;hr&gt;
&lt;h3 id=&#34;assessing-arterial-stiffness&#34;&gt;Assessing Arterial Stiffness&lt;/h3&gt;
&lt;p&gt;&lt;a href=&#34;https://journals.physiology.org/cms/10.1152/ajpheart.00218.2019/asset/images/large/zh40101929420004.jpeg&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;img src=&#34;https://journals.physiology.org/cms/10.1152/ajpheart.00218.2019/asset/images/large/zh40101929420004.jpeg&#34; alt=&#34;&#34;&gt;&lt;/a&gt;&lt;/p&gt;
&lt;hr&gt;
&lt;h3 id=&#34;results&#34;&gt;Results&lt;/h3&gt;
&lt;p&gt;&lt;a href=&#34;https://journals.physiology.org/cms/10.1152/ajpheart.00218.2019/asset/images/large/zh40101929420009.jpeg&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;img src=&#34;https://journals.physiology.org/cms/10.1152/ajpheart.00218.2019/asset/images/large/zh40101929420009.jpeg&#34; alt=&#34;&#34;&gt;&lt;/a&gt;&lt;/p&gt;
&lt;hr&gt;
&lt;h3 id=&#34;implications&#34;&gt;Implications&lt;/h3&gt;
&lt;ol&gt;
&lt;li&gt;Age range&lt;/li&gt;
&lt;li&gt;Influence of HR and SV.&lt;/li&gt;
&lt;/ol&gt;
&lt;hr&gt;
&lt;h3 id=&#34;questions&#34;&gt;Questions&lt;/h3&gt;
&lt;ol&gt;
&lt;li&gt;What would you think of using this technology to assess vascular age?&lt;/li&gt;
&lt;li&gt;How might it compare to other technologies?&lt;/li&gt;
&lt;li&gt;How could one assess the relative performance of such technologies?&lt;/li&gt;
&lt;/ol&gt;
&lt;hr&gt;
&lt;h3 id=&#34;next-steps&#34;&gt;Next Steps&lt;/h3&gt;
&lt;p&gt;&lt;em&gt;Assessing Vascular Age from the Photoplethysmogram: A Systematic Review from VascAgeNet&lt;/em&gt;&lt;/p&gt;
&lt;hr&gt;
&lt;h1 id=&#34;part-3&#34;&gt;Part 3&lt;/h1&gt;
&lt;h2 id=&#34;case-study-changes-in-pulse-pressure-amplification-with-age&#34;&gt;Case Study: Changes in Pulse Pressure Amplification with Age&lt;/h2&gt;
&lt;hr&gt;
&lt;h3 id=&#34;pulse-pressure-amplification&#34;&gt;Pulse Pressure Amplification&lt;/h3&gt;
&lt;p&gt;$$\mathrm{Pulse \ Pressure \ Amplification} = \frac{\mathrm{brachial \ pulse \ pressure}}{\mathrm{aortic \ pulse \ pressure}}$$&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Questions:&lt;/strong&gt;&lt;/p&gt;
&lt;ol&gt;
&lt;li&gt;How does pulse pressure amplification change with age?&lt;/li&gt;
&lt;li&gt;Why?&lt;/li&gt;
&lt;/ol&gt;
&lt;hr&gt;
&lt;h3 id=&#34;methods&#34;&gt;Methods&lt;/h3&gt;
&lt;p&gt;Investigated the effects of age on:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;Early systolic amplification (P1)&lt;/li&gt;
&lt;li&gt;Late systolic pressure augmentation (P2)&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;at the aorta.&lt;/p&gt;
&lt;hr&gt;
&lt;h3 id=&#34;results-1&#34;&gt;Results&lt;/h3&gt;
&lt;p&gt;&lt;a href=&#34;https://journals.physiology.org/cms/10.1152/ajpheart.00218.2019/asset/images/large/zh40101929420008.jpeg&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;&lt;img src=&#34;https://journals.physiology.org/cms/10.1152/ajpheart.00218.2019/asset/images/large/zh40101929420008.jpeg&#34; alt=&#34;&#34;&gt;&lt;/a&gt;&lt;/p&gt;
&lt;hr&gt;
&lt;h3 id=&#34;implications-1&#34;&gt;Implications&lt;/h3&gt;
&lt;p&gt;The database can be used to gain insight into the CV determinants of mechanisms of blood flow.&lt;/p&gt;
&lt;ol&gt;
&lt;li&gt;When might this be helpful?&lt;/li&gt;
&lt;li&gt;How should this approach be used:
&lt;ul&gt;
&lt;li&gt;instead of clinical studies&lt;/li&gt;
&lt;li&gt;as well as clinical studies, or&lt;/li&gt;
&lt;li&gt;not at all?&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;/ol&gt;
&lt;hr&gt;
&lt;h3 id=&#34;related-work&#34;&gt;Related Work&lt;/h3&gt;
&lt;p&gt;See the following for similar work, investigating the accuracy of methods for assessing pulse wave velocity:&lt;/p&gt;
&lt;p&gt;Willemet M &lt;em&gt;et al.&lt;/em&gt;, &lt;em&gt;A database of virtual healthy subjects to assess the accuracy of foot-to-foot pulse wave velocities for estimation of aortic stiffness&lt;/em&gt;, doi: &lt;a href=&#34;https://doi.org/10.1152/ajpheart.00175.2015&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;10.1152/ajpheart.00175.2015&lt;/a&gt;&lt;/p&gt;
&lt;hr&gt;
&lt;h1 id=&#34;part-4&#34;&gt;Part 4&lt;/h1&gt;
&lt;h2 id=&#34;potential-studies-using-blood-flow-modelling&#34;&gt;Potential studies using blood flow modelling&lt;/h2&gt;
&lt;hr&gt;
&lt;h3 id=&#34;exploring-potential-studies&#34;&gt;Exploring potential studies&lt;/h3&gt;
&lt;p&gt;Think of a study in which pulse wave modelling could be useful.&lt;/p&gt;
&lt;p&gt;Consider:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;Research question&lt;/li&gt;
&lt;li&gt;What would need to be simulated?&lt;/li&gt;
&lt;li&gt;Under what conditions?&lt;/li&gt;
&lt;li&gt;In which ways would the model need to be particularly accurate?&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;h3 id=&#34;limitations&#34;&gt;Limitations&lt;/h3&gt;
&lt;ul&gt;
&lt;li&gt;Dependent on model accuracy&lt;/li&gt;
&lt;li&gt;Which in turn, is dependent on input parameters&lt;/li&gt;
&lt;li&gt;Often requires specialist knowledge to perform studies&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;h3 id=&#34;benefits&#34;&gt;Benefits&lt;/h3&gt;
&lt;ul&gt;
&lt;li&gt;Allows pulse waves to be simulated under different conditions&lt;/li&gt;
&lt;li&gt;Control of physiology&lt;/li&gt;
&lt;li&gt;Free of measurement error&lt;/li&gt;
&lt;li&gt;Potentially cheap, and doesn&amp;rsquo;t require participant involvement&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;h3 id=&#34;opportunities&#34;&gt;Opportunities&lt;/h3&gt;
&lt;ul&gt;
&lt;li&gt;Preliminary pilot work in technology development&lt;/li&gt;
&lt;li&gt;Inform the design of &lt;em&gt;in vivo&lt;/em&gt; studies&lt;/li&gt;
&lt;li&gt;Understand the potential shortcomings of existing technologies&lt;/li&gt;
&lt;li&gt;Understand the mechanisms underlying haemodynamic observations&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;h3 id=&#34;further-resources&#34;&gt;Further Resources&lt;/h3&gt;
&lt;p&gt;See the following:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href=&#34;https://peterhcharlton.github.io/publication/simulating_pulse_waves/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Accompanying article&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://peterhcharlton.github.io/pwdb/pwdb.html&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Database&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://github.com/peterhcharlton/pwdb/wiki&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;User Manual&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://github.com/peterhcharlton/pwdb/wiki/Case-Studies&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Code for case studies&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;h2 id=&#34;acknowledgment&#34;&gt;Acknowledgment&lt;/h2&gt;
&lt;p&gt;None of this would have been possible without:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href=&#34;http://haemod.uk/members/ja&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Dr Jordi Alastruey-Arimon&lt;/a&gt;, who provided the &lt;a href=&#34;http://haemod.uk/nektar&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;model&lt;/a&gt; and supervision&lt;/li&gt;
&lt;li&gt;The British Heart Foundation, who funded the work&lt;/li&gt;
&lt;li&gt;COST Action CA18216 &amp;ldquo;Network for Research in Vascular Ageing&amp;rdquo; supported by COST (European Cooperation in Science and Technology)&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;h2 id=&#34;thank-you&#34;&gt;Thank you&lt;/h2&gt;
&lt;p&gt;&lt;a href=&#34;https://peterhcharlton.github.io/talk/introduction-to-modelling-arterial-pulse-waves/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;peterhcharlton.github.io&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&lt;em&gt;&lt;strong&gt;See this website for resources.&lt;/strong&gt;&lt;/em&gt;&lt;/p&gt;
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